Home
Class 11
MATHS
Insert 4 geometric means between 1 and 2...

Insert 4 geometric means between 1 and 243.

Text Solution

Verified by Experts

Let `G_(1),G_(2),G_(3)andG_(4)` be the geometric means
`therefore1,G_(1),G_(2),G_(3)G_(4),243` are in G.P.
`a=1,r=?,T_(6)=243`
Now `T_(6)=243rArrar^(5)=243rArr1.r^(5)=3^(5)rArrr=3`
`G_(1)=a.r=1.3,G_(2)=3.3=9,G_(3)=9.3=27,G_(4)=27.3=81`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    SUBHASH PUBLICATION|Exercise solved example (FIVE MARKS QUESTIONS WITH ANSWERS)|9 Videos
  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise FIVE MARKS QUESTIONS WITH ANSWERS|8 Videos
  • SETS

    SUBHASH PUBLICATION|Exercise THREE MARKS QUESETION WITH ANSWERERS|15 Videos

Similar Questions

Explore conceptually related problems

Insert 3 arithmetic means between 8 and 24.

Let A_(1),A_(2),A_(3),"......."A_(m) be arithmetic means between -3 and 828 and G_(1),G_(2),G_(3),"......."G_(n) be geometric means between 1 and 2187. Product of geometric means is 3^(35) and sum of arithmetic means is 14025. The value of n is

Let A_(1),A_(2),A_(3),"......."A_(m) be arithmetic means between -3 and 828 and G_(1),G_(2),G_(3),"......."G_(n) be geometric means between 1 and 2187. Product of geometric means is 3^(35) and sum of arithmetic means is 14025. The value of m is

Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the geometric mean between a and b.

Insert 3 arithmetic means between 8 & 24 .

Insert five geimetrec means between (1)/(3) and 9 and verify that their product is the fifth power of the geometric mean between (1)/(3) and 9.

If m is the A.M. of two distinct real numbers l and n ( l , n gt 1) and G_(1) , G_(2) and G_(3) are three geometric means between l and n , then G_(1)^(4) + 2 G_(2)^(4) + G_(3)^(4) equals :

If m is the A.M of two distinct real number l and n (l,n gt 1) and G_(1),G_(2) and G_(3) are three geometric means between l and n, then G_(1)^(4) + 2G_(2)^(4) + G_(3)^(4) equal :

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G1, G2 and G3 are three geometric means between l and n, then G1 4+2G2 4+G3 4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

Insert 6 harmonic means between 3 and (6)/(23)